Simplify the following expression: $r = \dfrac{-110p^3 - 44p^2}{99p^3}$ You can assume $p \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-110p^3 - 44p^2 = - (2\cdot5\cdot11 \cdot p \cdot p \cdot p) - (2\cdot2\cdot11 \cdot p \cdot p)$ The denominator can be factored: $99p^3 = (3\cdot3\cdot11 \cdot p \cdot p \cdot p)$ The greatest common factor of all the terms is $11p^2$ Factoring out $11p^2$ gives us: $r = \dfrac{(11p^2)(-10p - 4)}{(11p^2)(9p)}$ Dividing both the numerator and denominator by $11p^2$ gives: $r = \dfrac{-10p - 4}{9p}$